From Euclidean triangles to the hyperbolic plane
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Tarih
2022
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier Gmbh
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
We introduce a model of the hyperbolic plane which arises from Thurston's ideas on best Lipschitz maps between surfaces. More precisely, we apply Thurston's theory to the space of Euclidean triangles. We prove that the Lipschitz constant of the unique affine map between two Euclidean triangles induces a metric on the set of isometry classes of the triangles with area 1/2. We then prove that this space of triangles together with 2 times its natural metric is isometric to the hyperbolic plane. Our construction is simple and natural and it makes relations between several geometrical ideas. (C) 2021 Elsevier GmbH. All rights reserved.
Açıklama
Anahtar Kelimeler
Euclidean triangles, Lipschitz maps, Hyperbolic plane
Kaynak
Expositiones Mathematicae
WoS Q Değeri
Q3
Scopus Q Değeri
Q3
Cilt
40
Sayı
2
